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Proceedings of the American Mathematical Society

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The ideal class groups of two cyclotomic fields


Author: Frank Gerth
Journal: Proc. Amer. Math. Soc. 78 (1980), 321-322
MSC: Primary 12A35; Secondary 12A50
MathSciNet review: 553367
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Abstract: It is known that there are exactly two cyclotomic fields with class numbers equal to 8, namely the fields of 29th and 68th roots of unity. We show by elementary methods how to determine the structure of the ideal class groups of these fields.


References [Enhancements On Off] (What's this?)

  • [1] H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. Ia, Jber. Deutsch. Math.-Verein. 36 (1927), 233-311.
  • [2] John Myron Masley, Solution of small class number problems for cyclotomic fields, Compositio Math. 33 (1976), no. 2, 179–186. MR 0450229
  • [3] Edwin Weiss, Algebraic number theory, McGraw-Hill Book Co., Inc., New York-San Francisco-Toronto-London, 1963. MR 0159805

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0553367-5
Article copyright: © Copyright 1980 American Mathematical Society